In this paper, I explore whether elementary classical mechanics adheres to the Principle of Composition of Causes as Mill claimed and as certain contemporary authors still seem to believe. Among other things, I provide a proof that if one reads Mill’s description of the principle literally (as I think many do), it does not hold in any general sense. In addition, I explore a separate notion of Composition of Causes and note that it too does not hold in elementary classical mechanics. Among the major morals is that there is no utility to describing classical mechanics in terms of Composition of Causes. This is both because the stated principles do not hold and because when one describes what actually does hold in classical mechanics in terms of the Composition of Causes, one introduces misleading associations that can generate errors just as claimed by Russell (Mysticism and logic, 1981).